PSI - Issue 12
Yogesh Gandhi et al. / Procedia Structural Integrity 12 (2018) 429–437
432
Yogesh Gandhi et al. / Structural Integrity Procedia 00 (2018) 000 – 000
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3.2. ECTE model for SMA A model is needed to describe the SME behaviour of SMA wires that is accomplished here by a constitutive model based upon nonlinear thermo-elasticity and the definition of an effective coefficient of thermal expansion (ECTE) as proposed by Turner et al. (2007). The fundamental feature of the ECTE model is the axial constitutive relation for a SMA actuator, in which the non-mechanical (i.e., thermal and transformation) strains below the austenite start temperature (T
(1) where is the total axial strain of SMA-Composite Structure, is the effective coefficient of thermal expansion, and the subscript a indicates that the quantity is specific to the actuator material. It can be seen in Equation 1 that the ECTE model is intended to model thermally induced transformation phenomena, as opposed to stress induced (pseudo-elasticity), which is the restriction on ECTE model. It can be shown that the thermal strain in Equation 1 is governed by the usual thermoelastic effects at temperatures below the austenite start temperature and is related to the recovery stress at higher temperatures: i Y u g’ m du u f SMA m i , (2) The ECTE model was developed by Turner et al. to simulate a SMA Hybrid Composite (SMAHC) laminate where equations 1 or 2 where used, along with the corresponding ones for the transverse strains to build up the reduced stiffness matrix terms of the SMAHC ply, Q ij , and the thermoelastic effective strains (more details about the model can be found in the study by Turner et al. (2007)). In this work, the use of the ECTE model has been restricted to the axial direction to provide the stress-strain behaviour of SMA wires in a simplified manner that can be dealt with u i g A qu ™ f i u u -defined routine. Temperature-dependent orthotropic material properties for Nitinol are provided in table 2. Table 2. Temperature-dependent material properties for Nitinol (Turner et al. (2007)). Temperature, °C α 11 /°C E 11 , Pa ν 12 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 16 21 27 32 38 43 49 54 60 66 71 77 82 88 93 99 6.61E-06 6.61E-06 -3.09E-05 -3.87E-05 -5.04E-05 -5.57E-05 -1.01E-04 -1.35E-04 -1.42E-04 -1.34E-04 -1.20E-04 -1.05E-04 -9.93E-05 -9.90E-05 -9.72E-05 -9.13E-05 27170 27170 24800 22430 20060 25700 31340 36890 42620 48270 54860 61450 64210 63130 62060 63920
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